Order flow is toxic when it adversely selects market makers, who may be unaware they are providing liquidity at a loss. We present a new procedure to estimate flow toxicity based on volume imbalance and trade intensity (the VPIN toxicity metric). VPIN is updated in volume time, making it...

We investigate the implications of ambiguity aversion for performance and regulation of markets. In our model, agents' decision making may incorporate both risk and ambiguity, and we demonstrate that nonparticipation arises from the rational decision by some traders to avoid ambiguity. In...

Using the model structure of Easley and O'Hara, we demonstrate how the parameters of the market-maker's beliefs can be estimated from trade data. We show how to extract information from both trade and no-trade intervals, and how intraday and interday data provide information. We derive and...